Make Curve Have A Fill and Border
Since curves can't be rigged, the only way I see it is using Hooks.

Enter Edit Mode and hook each separate curve vertex you wish to move independently to a new object using the option Hook to new Object.



Then go into the second curve and repeat the process. For vertex you want to move together first select a existing empty you wish to hook it to, then enter Edit Mode, select said vertex and use the other option Hook to selected object.



If two vertex from different curves are hooked to the same empty they will move together. If you still want some independence occasionally you can always hook to separate empties, the parent two empties to a third "controller" empty that moves both simultaneously.